SIDIS transverse spin azimuthal asymmetries at COMPASS: Multidimensional analysis
SSIDIS transverse spin azimuthal asymmetries atCOMPASS: Multidimensional analysis
Bakur Parsamyan ∗ † University of Turin and Torino Section of INFNVia P. Giuria 1, 10125 Torino, ItalyE-mail: [email protected]
Exploration of transverse spin structure of the nucleon via study of the spin (in)dependent az-imuthal asymmetries in semi-inclusive deep inelastic scattering (SIDIS) and Drell-Yan (DY) re-actions is one of the main aspects of the broad physics program of the COMPASS experiment(CERN, Switzerland). In past decade COMPASS has collected a considerable amount of polar-ized deuteron and proton SIDIS data, while recent 2014 and 2015 runs were dedicated to theDrell-Yan measurements. Results on SIDIS azimuthal effects provided so far by COMPASS playan important role in general understanding of the three-dimensional nature of the nucleon. Givingaccess to the entire "twist-2" set of transverse momentum dependent (TMD) parton distributionfunctions (PDFs) and fragmentation functions (FFs) COMPASS data are being widely used inphenomenological analyses and experimental data fits. Recent unique and first ever x- Q -z-pTmultidimensional results for transverse spin asymmetries obtained by COMPASS serve as a directand unprecedented input for one of the hottest topics in the field of spin-physics: the TMD Q -evolution related studies. In addition, extraction of the Sivers and all other azimuthal effects fromfirst ever polarized Drell-Yan data collected recently by COMPASS will reveal another side ofthe spin-puzzle clarifying the link between SIDIS and Drell-Yan branches. This will be a uniquepossibility to test predicted universality and key-features of TMD PDFs using essentially the sameexperimental setup and exploring the same kinematical domain. In this review main focus willbe given to the very recent results from COMPASS multi-dimensional analysis of transverse spinasymmetries and to the physics aspects of COMPASS polarized Drell-Yan program. QCD Evolution 2015 -QCDEV2015-26-30 May 2015Jefferson Lab (JLAB), Newport News Virginia, USA ∗ Speaker. † on behalf of the COMPASS collaboration. c (cid:13) Copyright owned by the author(s) under the terms of the Creative CommonsAttribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). http://pos.sissa.it/ a r X i v : . [ h e p - e x ] D ec IDIS TSAs at COMPASS: Multi-D analysis
Bakur Parsamyan
1. Introduction
Schematic view of the SIDIS framework and some notations and definitions adopted in thisletter such as coordinate system, azimuthal angles, etc. are presented in Figure 1. In this frameworkthe target transverse polarization ( S T ) is defined relative to the virtual photon momentum direction,which is the most natural basis from the theoretical point of view. However, in experiment target isbeing polarized in laboratory system and transverse polarization ( P T ) is defined relative to the beam(incoming lepton) direction. As it was demonstrated in [1]-[4] this difference influences azimuthaldistributions in the final state. After applying appropriate conversions, the model-independentexpression for the SIDIS cross-section for transversely (w.r.t. lepton beam) polarized target can bere-written in the following way [1]-[4]: d σ dxdydzp hT d p hT d φ h d φ S = (cid:20) cos θ − sin θ sin φ S (cid:21) (cid:20) α xyQ y ( − ε ) (cid:18) + γ x (cid:19)(cid:21) ( F UU , T + ε F UU , L ) (1.1) × (cid:40) + (cid:112) ε ( + ε ) A cos φ h UU cos φ h + ε A cos ( φ h ) UU cos ( φ h ) + λ (cid:112) ε ( − ε ) A sin φ h LU sin φ h + P T (cid:113) − sin θ sin φ S (cid:34) (cid:18) cos θ A sin ( φ h − φ S ) UT +
12 sin θ (cid:112) ε ( + ε ) A sin φ h UL (cid:19) sin ( φ h − φ S )+ (cid:18) cos θ ε A sin ( φ h + φ S ) UT +
12 sin θ (cid:112) ε ( + ε ) A sin φ h UL (cid:19) sin ( φ h + φ S )+ cos θ ε A sin ( φ h − φ S ) UT sin ( φ h − φ S )+ cos θ (cid:112) ε ( + ε ) A sin φ S UT sin φ S + (cid:18) cos θ (cid:112) ε ( + ε ) A sin ( φ h − φ S ) UT +
12 sin θ ε A sin2 φ h UL (cid:19) sin ( φ h − φ S )+
12 sin θ ε A sin2 φ h UL sin ( φ h + φ S ) (cid:35) + P T λ (cid:113) − sin θ sin φ S (cid:34) (cid:18) cos θ (cid:113) ( − ε ) A cos ( φ h − φ S ) LT +
12 sin θ (cid:112) ε ( − ε ) A cos φ h LL (cid:19) cos ( φ h − φ S )+ (cid:18) cos θ (cid:112) ε ( − ε ) A cos φ S LT + sin θ (cid:113) ( − ε ) A LL (cid:19) cos φ S + (cid:16) cos θ (cid:112) ε ( − ε ) A cos ( φ h − φ S ) LT (cid:17) cos ( φ h − φ S )+
12 sin θ (cid:112) ε ( − ε ) A cos φ h LL cos ( φ h + φ S ) (cid:35)(cid:41) where ε = ( − y − γ y ) / ( − y + y + γ y ) and γ = Mx / Q and θ is the angle between beamand virtual photon momentum directions (see Figure 1). When compared with the "standard" cross-section [5], in which the effects due to the P T to S T transition have been neglected, 1.2 contains new sin θ -scaled terms and θ -depending factors and two extra azimuthal modulations (sin ( ϕ h + ϕ S ) and cos ( ϕ h + ϕ S ) ) related to longitudinal amplitudes (these two amplitudes have been measured tobe compatible with zero and are not going to be discussed in this letter).Beside those two terms, the expression 1.2 counts in total eight more w i ( φ h , φ S ) azimuthalmodulations. Each of this effects leads to a A w i ( φ h , φ S ) BT Transverse-Spin-dependent Asymmetry all "new" terms are underlined and marked in green. IDIS TSAs at COMPASS: Multi-D analysis
Bakur Parsamyan (TSA) defined as a ratio of the associated structure function F w i ( φ h , φ S ) BT to the azimuth-independentone F UU = F UU , T + ε F UU , L . Here the superscript of the asymmetry indicates corresponding modu-lation, the first and the second subscripts - respective ("U"-unpolarized, "L"-longitudinal and "T"-transverse) polarization of beam and target. Five amplitudes which depend only on target polariza-tion are the target Single-Spin Asymmetries (SSA), the other three which depend also on λ beamlongitudinal polarization are known as Double-Spin Asymmetries (DSA). -0.0500.05 -0.0500.05 -0.0500.05 -0.0500.05 -0.0500.05 -0.0500.05 -0.0500.05 -0.0500.05 -0.0500.05 -0.0500.05 -0.0500.05 -0.0500.05-0.0500.05 -0.0500.05 -0.0500.05 -0.0500.05 -0.0500.05 -0.0500.05 l q q z’l’ zxlepton planex’ y zx l'l S T p h φ h φ S q p hT Figure 1:
SIDIS process framework.
As it can be seen from 1.2 in several cases TSAsare being mixed with sin θ -scaled longitudinal am-plitudes. Since sin θ is a rather small quantity inCOMPASS kinematics [6] the influence of the addi-tional to the TSAs terms, represented by sin θ -scaledlongitudinal-spin amplitudes and θ -angle dependentfactors, is sizable only in the case of A cos ϕ S LT DSA,which, even taking into account the smallness of sin θ ,is still sizably affected by a large A LL amplitude [7]. Tocorrect the A cos ϕ S LT asymmetry we have used the A LL val-ues evaluated based on [8]) which are in close agree-ment with the data [6, 7].In the QCD parton model approach four ofthe eight transverse spin asymmetries ( A sin ( φ h − φ S ) UT , A sin ( φ h + φ S ) UT , A sin ( φ h − φ s ) UT SSAs and A cos ( φ h − φ s ) LT DSA)have Leading Order (LO) or leading-twist interpreta-tion. The first two are the "Sivers" and "Collins" ef-fects [9]–[11] which are the most studied ones. Theseasymmetries are given as convolutions of: f ⊥ q T SiversPDF with D h q ordinary FF, and h q "transversity" PDF with the H ⊥ h q Collins FF, respectively. Theother two LO terms are the A sin ( φ h − φ S ) UT single-spin asymmetry (related to h ⊥ q T ("pretzelosity") PDF[12]–[17]) and A cos ( φ h − φ S ) LT DSA (related to g q T ("worm-gear") distribution function [12]–[18],[8]).Remaining four asymmetries are so-called "higher-twist" effects . Corresponding structurefunctions enter at sub-leading order ( Q − ) and contain terms given as various mixtures of twist-two and twist-three (induced by quark-gluon correlations) parton distribution and fragmentationfunctions [2]–[20]. However, applying wildly used "Wandzura-Wilczek approximation" this highertwist objects can be simplified to the twist-two order (see [2, 3] for more details). Complete list of"twist-two"-level interpretations for all eight TSAs is quoted in 1.2. A sin ( φ h − φ S ) UT ∝ f ⊥ q T ⊗ D h q , A sin ( φ h + φ S ) UT ∝ h q ⊗ H ⊥ h q , (1.2) A sin ( φ h − φ S ) UT ∝ h ⊥ q T ⊗ H ⊥ h q , A cos ( φ h − φ S ) LT ∝ g q T ⊗ D h q A sin ( φ S ) UT ∝ Q − ( h q ⊗ H ⊥ h q + f ⊥ q T ⊗ D h q ) , A sin ( φ h − φ S ) UT ∝ Q − ( h ⊥ q T ⊗ H ⊥ h q + f ⊥ q T ⊗ D h q ) , A cos ( φ S ) LT ∝ Q − ( g q T ⊗ D h q ) , A cos ( φ h − φ S ) LT ∝ Q − ( g q T ⊗ D h q ) . The whole set of eight SIDIS asymmetries has been already measured at COMPASS for bothdeuteron and proton targets (See [9]–[17] and references therein). in equations 1.2–1.4 the twist-2 amplitudes are marked in red and higher-twist ones in blue IDIS TSAs at COMPASS: Multi-D analysis
Bakur Parsamyan
Using similar notations, single-polarized ( π N ↑ ) Drell-Yan cross-section at leading order canbe written in the following model-independent way [21]: d σ LO d Ω = α em Fq F U (cid:110) + cos θ + sin θ A cos2 ϕ CS U cos 2 ϕ CS + S T (cid:104)(cid:0) + cos θ (cid:1) A sin ϕ S T sin ϕ S (1.3) + sin θ (cid:16) A sin ( ϕ CS + ϕ S ) T sin ( ϕ CS + ϕ S ) + A sin ( ϕ CS − ϕ S ) T sin ( ϕ CS − ϕ S ) (cid:105)(cid:17)(cid:111) . Here ϕ CS and ϕ S angular variables are defined in "Collins-Soper" and "target rest" frames, cor-respondingly (see Figure 2). Similarly to the SIDIS case, "U", "L" and "T" subscripts denote thestate of the target polarization while the superscript indicates the corresponding modulation. -0.050 -0.050 -0.050 -0.050 -0.050 -0.050 -0.050 -0.050 -0.050 -0.050 -0.050 -0.050 -0.050 -0.050 -0.050 -0.050 S T qq T H a ( P a ) x ˆ y ˆ z ˆ φ S θ CS ℓ P a , CS P b , CS x ˆ CS z ˆ CS y ˆ CS ℓ ′ φ CS Figure 2:
Drell-Yan process framework.
As one can see, at LO the DY cross-section con-tains only one unpolarized and three target transversespin dependent azimuthal asymmetries. Within thesame QCD parton model approach, at variance withthe SIDIS-case, Drell-Yan asymmetries are interpretedas convolutions of two TMD PDFs, one of the the"beam" and one of the "target" hadron. Quoting onlythe target nucleon PDFs: the A sin ϕ s T , A sin ( ϕ CS − ϕ s ) T and A sin ( ϕ CS + ϕ s ) T give access to the "Sivers" f ⊥ q T , "transver-sity" h q and "pretzelosity" h ⊥ q T , distribution functions,respectively. Within the QCD-concept of generalizeduniversality of TMD PDFs it appears that same partondistribution functions can be accessed both in SIDISand Drell-Yan (see the Table. 1 for the complete list).Therefore, future COMPASS results on DY asymme-tries are intriguingly complementary to the results pre-viously obtained by the same collaboration for az-imuthal effects in SIDIS. The comparison of two setswill give an unprecedented opportunity to access TMDPDFs via two mechanisms and test their universality and key features (for instance, predicted Siversand Boer-Mulders PDFs sign change) using essentially same experimental setup.SIDIS (cid:96) → N ↑ TMD PDF DY π N ↑ (LO) A cos2 φ h UU , A cos φ h UU h ⊥ q A cos2 ϕ CS U A sin ( φ h − φ s ) UT , A sin φ s UT , A sin ( φ h − φ s ) UT f ⊥ q T A sin ϕ S T A sin ( φ h + φ s − π ) UT , A sin φ s UT h q A sin ( ϕ CS − ϕ S ) T A sin ( φ h − φ s ) UT , A sin ( φ h − φ s ) UT h ⊥ q T A sin ( ϕ CS + ϕ S ) T A cos ( φ h − φ s ) LT , A cos φ s LT , A cos ( φ h − φ s ) LT g q T double-polarized DY Table 1:
Nucleon TMD PDFs accessed via SIDIS and Drell-Yan azymmetries. IDIS TSAs at COMPASS: Multi-D analysis
Bakur Parsamyan
Another hot topic being addressed by the COMPASS collaboration is the multi-differentialanalysis of SIDIS data. In general, asymmetries being represented as convolutions of differentTMD distribution functions are considered to be complex objects a priori dependent on the ex-perimental choice of multidimensional kinematical phase-space. Thus, in order to reveal the mostcomplete multivariate dependence of TMD PDFs, it is important to extract azimuthal amplitudes asmulti-differential functions of kinematical variables. In practice, available experimental data oftenare too limited for such an ambitious approach and studying dependence of the asymmetries onsome specific kinematic variable one is forced to stick to one-dimensional case integrating over allthe other variables. -2
10 10 p S i v A -0.0500.050.1 COMPASS 2010 proton data x -2 -1 z h (GeV/ c ) T p p C o ll A -0.1-0.0500.050.1 HERMES p + PLB 693 (2010) rescaled by (1-
Figure 3:
Sivers (top) and Collins (bottom) asymmetries at COMPASS and HERMES.
Presently, one of the related challenges in the field of spin-physics is the study of TMD evolu-tion of various PDFs and FFs and related asymmetries. Comparison of COMPASS and HERMESresults for Sivers and Collins asymmetries on proton [9, 22, 23] emphasized the importance of thisdomain. In the Figure 3 are demonstrated Sivers (top) and Collins (bottom) asymmetries for posi-tive hadrons as measured at COMPASS and HERMES experiments. While results for the Collinsasymmetries appear to be compatible, Sivers effect at COMPASS at large x is noticeably smallerthan the one obtained by HERMES. Here the important detail is that at given x COMPASS Q values are by a factor of 3 − Q -dependence of TMDs. Presentlydifferent models predict from small up to quite large QCD-evolution effects attempting to describeavailable experimental observations and make predictions for the future ones [24]–[26]. Additionalprecise experimental measurements exploring different Q domains for fixed x -range are necessaryto further constrain the theoretical models. The work described in this review is a unique and first5 IDIS TSAs at COMPASS: Multi-D analysis
Bakur Parsamyan ever attempt to explore behaviour of TSAs in the multivariate kinematical environment of the datacollected by a single experiment. For this purpose COMPASS experimental data was split into fivedifferent Q ranges giving an opportunity to study asymmetries as a function of Q at fixed bins of x . Additional variation of z and p T cuts allows to deeper explore multi-dimensional behaviour ofthe TSAs and their TMD constituents.
2. Multidimensional analysis of TSAs
During the "phase-1" (from 2002 to 2010) COMPASS has performed series of SIDIS data-takings using 160 GeV/c longitudinally polarized muon beam and transversely polarized LiD and NH targets (See [10]–[17] and references therein). In 2012 COMPASS entered in "phase-II" andrecently performed Drell-Yan measurements with 190 GeV/c π − beam and unpolarized (in 2014)and transversely polarized NH -targets (in 2015) [14, 21].Very soon both sets of COMPASS results from SIDIS and Drell-Yan will become a subject ofglobal fits and phenomenological analyses. In order to do provide relevant input for these studies,COMPASS SIDIS proton 2010 data has been re-analyzed in a more differential way extractingthe asymmetries in the same four Q kinematic regions which were selected for the COMPASSDrell-Yan measurement program [14, 21]: Q / ( GeV / c ) ∈ [
1; 4 ] , [
4; 6 . ] , [ .
25; 16 ] , [
16; 81 ] . Pre-liminary results obtained with this selection have been presented in [12, 14] while current reviewis dedicated to more recent x - z - p T - Q multi-dimensional approach [13].The analysis was carried out on the same data-sample collected in 2010 with transverselypolarized proton target. General event selection as well as asymmetry extraction and systematicuncertainty evaluation procedures were identical to those used for recent COMPASS results onCollins, Sivers and other TSAs [10]–[17]. Figure 4:
COMPASS x : Q (left) and z : p T (right) phase space coverage. Amplitudes for all ten azimuthal modulations present in the transverse spin dependent part ofthe cross-section 1.2 have been extracted simultaneously using extended unbinned maximum like-lihood estimator. Obtained "raw" asymmetries have been then corrected for average depolarizationfactors ( ε -depending factors in equation 1.2 standing in front of the amplitudes), dilution factorand target and beam (only DSAs) polarizations evaluated in the given kinematical bin [10]–[17].Primary sample is defined by the following standard DIS cuts: Q > ( GeV / c ) , 0 . < x < . . < y < . hadronic selections: p T > . z > . IDIS TSAs at COMPASS: Multi-D analysis
Bakur Parsamyan
In order to study possible Q -dependence the x : Q phase-space covered by COMPASS exper-imental data has been divided into 5 × Q -ranges are the following ones: Q / ( GeV / c ) ∈ [
1; 1 . ] , [ .
7; 3 ] , [
3; 7 ] , [
7; 16 ] , [
16; 81 ] . Inaddition, each of this samples has been divided into five z and five p T (GeV/c) sub-ranges definedas follows: z > . z > .
2, 0 . < z < .
2, 0 . < z < . . < z < . p T > .
1, 0 . < p T < .
75, 0 . < p T < .
3, 0 . < p T < .
75 and p T > . x -dependence in Q - z and Q - p T grids. 2) Q -dependence in x - z and x - p T grids. 3) Q - (or x -) dependence in x - p T (or Q - p T ) grids withdifferent choices of z sub-range.The second general approach was defined to focus on z - and p T -dependences in different x -ranges. For this study, two-dimensional z : p T phase-space has been divided into 7 × x -ranges: 0 . < x < .
7, 0 . < x < . . < x < .
7, asymmetries have been extracted in "3D: x - z - p T "grids. In the next section selected COMPASS preliminary results obtained for multi-dimensionaltarget transverse spin dependent azimuthal asymmetries are presented.
3. Results As an example of "3D" Sivers and Collins effects, results for the extracted x - z - Q configura-tions are presented in the Figure 5 (’top’ and ’bottom’ plots, respectively). As a general observation,for positive hadron production Sivers asymmetry shows sizable signal along whole x -range, whilefor negative hadrons effect is not clear. Still, there are some indications for a positive Sivers sig-nal at relatively large x and Q and for a negative effect at low x . Clear "mirrored" behaviour forpositive and negative hadron amplitudes is being observed in most of the bins for Collins effect. Ingeneral, both Sivers and Collins amplitudes tend to increase in absolute value with z and p T .Demonstrated in the Figure 5 Q -dependences of Sivers and Collins asymmetries serve as adirect input for TMD-evolution related studies. In fact, for Sivers effect in several x-bins thereare some hints for possible decreasing Q -dependence for positive hadrons which become moreevident at large z . In the meantime, Collins asymmetry does not show any clear indications for Q -dependence. Thus, both these observations are in agreement with quoted previously COMPASS-HERMES comparison for Sivers and Collins effects (see [9, 22, 23] and Figure 3).Another SSA which is found to be non-zero at COMPASS is the A sin ( φ s ) UT term which is pre-sented in Figure 6 (top) in "3D: x - z - p T " configuration. Here the most interesting is the large z -rangewere amplitude is measured to be sizable and non zero both for positive and negative hadrons. Itis relevant to remind that within the "Wandzura-Wilczek approximation" this asymmetry can beassociated with Sivers and Collins mechanisms.The bottom plot in the Figure 6 is dedicated to the A cos ( φ h − φ S ) LT DSA explored in "3D: Q - z - x " grid and superimposed with the theoretical curves from [18]. This is the only DSA whichappears to be non-zero at COMPASS and the last TSA for which a statistically significant signal Results discussed in this section have been first presented at the SPIN-2014 conference [13], see also [5],[27]. IDIS TSAs at COMPASS: Multi-D analysis
Bakur Parsamyan has been detected. Remaining four asymmetries are found to be small or compatible with zerowithin available statistical accuracy which is in agreement with available predictions [19, 20, 28].As an example the "3D: x - z - p T " results for A sin ( φ h − φ S ) UT asymmetry are presented in Figure 7.8 IDIS TSAs at COMPASS: Multi-D analysis
Bakur Parsamyan -0.0500.05 + h - h ) S f - h f s i n ( U T A T z>0.1; p -0.0500.05 ) S f - h f s i n ( U T A -0.0500.05 ) S f - h f s i n ( U T A -0.0500.05 ) S f - h f s i n ( U T A -0.0500.05 ) S f - h f s i n ( U T A -0.0500.05 ) S f - h f s i n ( U T A -0.0500.05 ) S f - h f s i n ( U T A -0.0500.05 ) S f - h f s i n ( U T A -0.0500.05 (GeV/c) Q ) S f - h f s i n ( U T A -0.0500.05 preliminaryCOMPASS >0.1 GeV/c T z>0.2; p -0.0500.05 -0.0500.05 -0.0500.05 -0.0500.05 -0.0500.05 -0.0500.05 -0.0500.05 -0.0500.05 (GeV/c) Q -0.0500.05 Proton 2010 data >0.1 GeV/c T -0.0500.05 -0.0500.05 -0.0500.05 -0.0500.05 -0.0500.05 -0.0500.05 -0.0500.05 -0.0500.05 (GeV/c) Q -0.0500.05 >0.1 GeV/c T -0.0500.05 -0.0500.05 -0.0500.05 -0.0500.05 -0.0500.05 -0.0500.05 -0.0500.05 -0.0500.05 (GeV/c) Q -0.0500.05 >0.1 GeV/c T -0.0500.05 -0.0500.05 -0.0500.05 -0.0500.05 -0.0500.05 -0.0500.05 -0.0500.05 -0.0500.05 (GeV/c) Q -0.100.1 + h - h ) p - S f + h f s i n ( U T A T z>0.1; p -0.100.1 ) p - S f + h f s i n ( U T A -0.100.1 ) p - S f + h f s i n ( U T A -0.100.1 ) p - S f + h f s i n ( U T A -0.100.1 ) p - S f + h f s i n ( U T A -0.100.1 ) p - S f + h f s i n ( U T A -0.100.1 ) p - S f + h f s i n ( U T A -0.100.1 ) p - S f + h f s i n ( U T A -0.100.1 (GeV/c) Q ) p - S f + h f s i n ( U T A -0.100.1 preliminaryCOMPASS >0.1 GeV/c T z>0.2; p -0.100.1 -0.100.1 -0.100.1 -0.100.1 -0.100.1 -0.100.1 -0.100.1 -0.100.1 (GeV/c) Q -0.100.1 Proton 2010 data >0.1 GeV/c T -0.100.1 -0.100.1 -0.100.1 -0.100.1 -0.100.1 -0.100.1 -0.100.1 -0.100.1 (GeV/c) Q -0.100.1 >0.1 GeV/c T -0.100.1 -0.100.1 -0.100.1 -0.100.1 -0.100.1 -0.100.1 -0.100.1 -0.100.1 (GeV/c) Q -0.100.1 >0.1 GeV/c T -0.100.1 -0.100.1 -0.100.1 -0.100.1 -0.100.1 -0.100.1 -0.100.1 -0.100.1 (GeV/c) Q Figure 5:
Sivers (top) and Collins (bottom) asymmetries in "3D" x - z - Q . IDIS TSAs at COMPASS: Multi-D analysis
Bakur Parsamyan -0.0500.05 + h - h S f s i n U T A all x0.10
Top: A sin ( φ s ) UT asymmetry in "3D" ( x - z - p T ). Bottom: A cos ( φ h − φ S ) LT in "3D" ( Q - z - x ) superimposedwith theoretical predictions from [18]. IDIS TSAs at COMPASS: Multi-D analysis
Bakur Parsamyan -0.100.1 + h - h ) S f - h f s i n ( U T A all x0.10
4. Conclusions
COMPASS multidimensional analysis of the whole set of proton TSAs has been performedexploring various multi-differential configurations in the x : Q : z : p T phase-space. Particular atten-tion was focused on the possible Q -dependence of asymmetries, serving a direct input to TMD-evolution related studies. Several interesting observations have been made studying the resultsobtained for Sivers, Collins, A cos ( φ h − φ S ) LT and A sin ( φ S ) UT asymmetries. Other four asymmetries werefound to be compatible with zero within available statistical accuracy.This is the first ever attempt to extract multi-differential dependencies of all possible transversespin dependent asymmetries using experimental data collected by a single experiment. Providedhighly differential data set, combined with past and future relevant data of other collaborations, willgive a unique opportunity to access the whole set of TMD PDFs and test their multi-differentialnature.Also particularly interesting will be the planned comparison of presented SIDIS TSAs withthe Drell-Yan asymmetries which soon will be extracted from first ever polarized Drell-Yan datacollected by COMPASS in 2015. This unique opportunity to explore nucleon spin-structure viatwo different processes measured with the same experimental setup, will be the first direct chanceto test the universality and key features of TMD PDFs such as, for instance, expected "signchange" of the Sivers function. 11 IDIS TSAs at COMPASS: Multi-D analysis
Bakur Parsamyan
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